Let \(\mathbf {F}(\mathbf {x}):\mathbb {R}^n\rightarrow \mathbb {R}^n\)  be a vector of \(n\)  polynomials in \(n\)  variables. Our goal is to solve the system \(\mathbf {F}(\mathbf {x})=\mathbf {0}\) . To do so, we first construct a starting system \(\mathbf {G}(\mathbf {x})=\mathbf {0}\)  that can be easily solved. The only requirement on \(\mathbf {G}\)  is that it must have at least as many distinct solutions as \(\mathbf {F}\) . Several techniques to construct such a system exist. In this work, we use the so called polyhedral initialisation described in [1]}. Next, we can define the homotopy
\(\mathbf {H}(\mathbf {x}, t) = (1-t)\mathbf {F}(\mathbf {x}) + \gamma t\mathbf {G}(\mathbf {x}), \) 
